Q2. Solve :
(a) 2(x + 4) = 12 (c) 3(n – 5) = – 21
(e) 4(2 – x) = 8
Answers
Explanation:
A. 2(x+4)=12
2x+8=12
2x = 12 - 8
2x = 4
x = 2
B. 4(2 - x) = 8
8 - 4x = 8
- 4x = 8 - 8
- 4x = 0
x = 0
C. 3(n - 5) = -21
3n - 15 = - 21
3n = - 21 + 15
3n = -6
n = -2
Answer:
a) 2(x + 4) = 12
➨ 2x + 8 = 12 (distributive property over addition)
➨ 2x = 12 - 8 (transposing 8 to the RHS)
➨ 2x = 4
➨ x = 4/2 (transposing 2 to the RHS)
➨ x = 2
(Verification:
Putting x = 2:-
- 2(2 + 4) = 12
- 4 + 8 = 12
- 12 = 12
- LHS = RHS
Hence, verified!)
c) 3(n - 5) = -21
➨ 3n - 15 = -21 (distributive property over subtraction)
➨ 3n = -21 + 15 (transposing -15 to the RHS)
➨ 3n = -6
➨ n = -6/3 (transposing 3 to the RHS)
➨ n = -2
(Verification:
Putting n = -2:-
- 3(-2 - 5) = -21
- -6 - 15 = -21
- -21 = -21
- LHS = RHS
Hence, verified!)
(e) 4(2 - x) = 8
➨ 8 - 4x = 8 (distributive property over subtraction)
➨ -4x = 8 - 8 (transposing 8 to the RHS)
➨ -4x = 0
➨ x = 0/4 (transposing -4 to the RHS)
➨ x = 0
(Verification:
Putting x = 0,
- 4(2 - 0) = 8
- 8 - 0 = 8
- 8 = 8
- LHS = RHS
Hence, verified!)
Explanation:
- Transposition is a method where numerals are to be moved to the other side to get the value of the variable.
- The sign of the number changes when we transpose a number to the opposite side. For example, -4 becomes +4 and +2 becomes -2.